Multicarrier transmission system with reduced complexity channel response estimation

ABSTRACT

Described is a transmission system for transmitting a multicarrier signal from a transmitter ( 10 ) to a receiver ( 20 ). The multicarrier signal comprises a plurality of subcarriers. The receiver ( 20 ) comprises a channel estimator ( 28 ) for estimating amplitudes of the subcarriers and for estimating time derivatives of the amplitudes. The receiver ( 20 ) further comprises an equalizer ( 24 ) for canceling intercarrier interference included in the received multicarrier signal in dependence on the estimated amplitudes and derivatives ( 29 ). The channel estimator ( 28 ) comprises a reduced complexity filter for deriving vectors of the estimated amplitudes and derivatives ( 29 ) from vectors of received symbols ( 23 ) and vectors of estimated symbols ( 27 ). The reduced complexity filter may be arranged for exploiting an amplitude correlation between the amplitudes of different subcarriers and/or for exploiting a derivative correlation between the derivatives of different subcarriers.

[0001] The invention relates to a transmission system for transmitting amulticarrier signal from a transmitter to a receiver.

[0002] The invention further relates to a receiver for receiving amulticarrier signal from a transmitter, a channel estimator forestimating amplitudes of subcarriers included in a multicarrier signaland for estimating time derivatives of the amplitudes, and to a methodof estimating amplitudes of subcarriers included in a multicarriersignal and for estimating time derivatives of the amplitudes.

[0003] Multicarrier signal modulation methods, such as OFDM and MC-CDMA,have been around for some time now. OFDM or Orthogonal FrequencyDivision Multiplexing is a modulation method designed in the 1970's inwhich multiple user symbols are transmitted in parallel using differentsubcarriers. These subcarriers have overlapping (sinc-shaped) spectra,nonetheless the signal waveforms are orthogonal. Compared to modulationmethods such as BPSK, QPSK or MSK, OFDM transmits symbols which have arelatively long time duration, but a narrow bandwidth. Mostly, OFDMsystems are designed such that each subcarrier is small enough inbandwidth to experience frequency-flat fading. This also ensures thatthe subcarriers remain orthogonal when received over a (moderately)frequency selective but time-invariant channel. If the OFDM signal isreceived over such a channel, each subcarrier experiences a differentattenuation, but no dispersion.

[0004] The above mentioned properties of OFDM avoid the need for atapped delay line equalizer and have been a prime motivation to use OFDMmodulation methods in several standards, such as Digital AudioBroadcasting (DAB), the Digital Terrestrial Television Broadcast (DTTB)which is part of the Digital Video Broadcasting standard (DVB), and morerecently the wireless local area network standard HIPERLAN/2.Particularly in the DAB and DTTB applications, mobile reception underdisadvantageous channel conditions are foreseen, with both frequency andtime dispersion. Mobile reception of television has not been regarded asa major market up to now. Nonetheless, the DVB system promises to becomea high-speed delivery mechanism for mobile multimedia and internetservices. At the IFA '99 Consumer Electronics trade show, a consortiumof Nokia, Deutsche Telecom and ZDF demonstrated mobile web browsing,email access and television viewing over an OFDM DVB link, with a GSMreturn channel. With 8 k OFDM subcarriers, over the air DVB receptionfunctioned properly for vehicle speeds up to 50 mph. Mobile reception,i.e. reception over channels with Doppler spreads and the correspondingtime dispersion remains one of the problems associated with OFDM systemsin particular and multicarrier transmission systems in general. Whereasits robustness against frequency selectivity is seen as an advantage ofOFDM, the time-varying character of the channel is known to limit thesystem performance. Time variations are known to corrupt theorthogonality of the OFDM subcarrier waveforms. In such a case,Intercarrier Interference (ICI, also referred to as interchannelinterference or FFT leakage) occurs because signal components from onesubcarrier cause interference to other, mostly neighboring, subcarriers.

[0005] In the document “Equalization of FFT-leakage in mobile DVB-T”,Master Thesis in Radiocommunication from the Royal Institute ofTechnology, Stockholm, by Guillaume Geslin, April 1998, a multicarriertransmission system is disclosed. In this known transmission system ICIis cancelled (i.e. detected and removed from the received multicarriersignal) in the receiver by means of an equalizer. This equalizer derivesa vector of estimated symbols from a vector of received symbols. Theoperation of the equalizer is based upon a channel model in which theamplitudes of the subcarriers and the time derivatives thereof areindicative of the ICI. The receiver comprises a channel estimator whichgenerates estimates of these amplitudes and derivatives and suppliesthese estimates to the equalizer. The equalizer then cancels the ICI independence on the estimates of the amplitudes and derivatives. Thechannel estimator in the known transmission system is relativelycomplex, i.e. a relatively large number of computations is needed toimplement the channel estimator.

[0006] It is an object of the invention to provide a transmission systemaccording to the preamble in which the computational burden issubstantially reduced. This object is achieved in the transmissionsystem according to the invention, said transmission system beingarranged for transmitting a multicarrier signal from a transmitter to areceiver, the multicarrier signal comprising a plurality of subcarriers,the receiver comprising a channel estimator for estimating amplitudes ofthe subcarriers and for estimating time derivatives of the amplitudes,the receiver further comprising an equalizer for canceling intercarrierinterference included in the received multicarrier signal in dependenceon the estimated amplitudes and derivatives, wherein the channelestimator comprises a reduced complexity filter for deriving vectors ofthe estimated amplitudes and derivatives from vectors of receivedsymbols and vectors of estimated symbols. The invention is based uponthe recognition that the complexity of the channel estimator/filter canbe substantially reduced without seriously affecting the ICIcancellation procedure.

[0007] In an embodiment of the transmission system according to theinvention the reduced complexity filter is arranged for exploiting anamplitude correlation between the amplitudes of different subcarriersand/or for exploiting a derivative correlation between the derivativesof different subcarriers. Although the channel model is characterized by2N parameters (with N being the number of subcarriers), the number ofindependent degrees of freedom is substantially smaller in practice.This property comes from the fact that the propagation delay spread isoften much smaller than the word duration. This property also means thatthe entries in a vector of estimated amplitudes are strongly correlated,so that the covariance matrix C_(a) of the amplitudes may be accuratelyapproximated by a low-rank matrix. Similarly, the entries in a vector ofderivatives are strongly correlated and the covariance matrix C_(d) ofthe derivatives may also be accurately approximated by a low-rankmatrix. Using these low-rank matrices in the channel estimator/filterresults in a substantial reduction of the complexity.

[0008] In a further embodiment of the transmission system according tothe invention the amplitude correlation and/or the derivativecorrelation are characterized by a N×N matrix C, with N being the numberof subcarriers, wherein C=UΛU^(H), with U being the N×N unitary matrixof eigenvectors of C and Λ being the N×N positive diagonal matrix of theeigenvalues {Λ₁, . . . , Λ_(N)} of C, and wherein Λ is approximated by{Λ₁, . . . , Λ_(r), 0, . . . 0}, with r<<N. The covariance matricesC_(a) and C_(d) depend on the matrix C=UΛU^(H). The sequence ofeigenvalues {Λ₁, . . . , Λ_(N)} may be accurately approximated with arelatively small number r of non-zero values {Λ₁, . . . , Λ_(r),0, . . .0}.

[0009] In a further embodiment of the transmission system according tothe invention the reduced complexity filter comprises a multiplicationby the N×N leakage matrix Ξ, wherein the multiplication is implementedby a combination of an N-point IFFT and an N pointwise multiplier. Anadditional complexity reduction is caused by the fact that the leakagematrix Ξ is diagonalized by a Fourier basis, i.e. that Ξ=FΔF^(H), whereF is the N-point FFT matrix with normalized columns and Δ is a positivediagonal matrix. Hence, a multiplication by the N×N matrix Ξ may beimplemented by a combination of an N-point IFFT and N pointwisemultiplications and an N-point FFT, thereby substantially reducingcomplexity.

[0010] The above object and features of the present invention will bemore apparent from the following description of the preferredembodiments with reference to the drawings, wherein:

[0011]FIG. 1 shows a block diagram of a transmission system according tothe invention,

[0012]FIG. 2 shows a block diagram of a channel responseestimator/reduced complexity filter according to the invention.

[0013] The invention is based upon the development of a simple andreliable channel representation. Consider a multicarrier transmissionsystem, e.g. an OFDM or MC-CDMA transmission system, with N subcarriersspaced by ƒ_(s). Each subcarrier has a rectangular envelope of a finitelength that, including the cyclic extension, exceeds (1/ƒ_(s)). Lets=[S₁, . . . , S_(N)]^(T) be a vector of N transmitted symbols, then thetransmitted continuous time baseband signal may be written as follows:$\begin{matrix}{{x(t)} = {\sum\limits_{k = 1}^{N}{s_{k}{{\exp \left( {\quad 2\pi \quad f_{s}{kt}} \right)}.}}}} & (1)\end{matrix}$

[0014] In the case of a frequency selective time-varying additive whiteGaussian noise (AWGN) channel, the received continuous time signal maybe written as follows: $\begin{matrix}{{{y(t)} = {{\sum\limits_{k = 1}^{N}{s_{k}{H_{k}(t)}{\exp \left( {{2\pi}\quad f_{s}{kt}} \right)}}} + {n(t)}}},} & (2)\end{matrix}$

[0015] wherein the coefficient H_(k)(t) represents the time-varyingfrequency response at the k-th subcarrier, for 1≦k≦N, and wherein n(t)is AGWN within the signal bandwidth. We assume that the channel slowlyvaries so that only a first order variation may be taken into accountwithin a single data block duration. In other words, we assume thatevery H_(k)(t) is accurately approximated by

H _(k)(t)≈H _(k)(t _(r))+H _(k) ^(′)(t _(r))(t−t _(r)),  (3)

[0016] wherein H_(k) ^(′)(t) is the first order derivative of H_(k)(t)and wherein t_(r) is a reference time within the received data block.Note that the time varying channel H_(k)(t) may also take into account aresidual frequency offset, after the coarse frequency synchronization.

[0017] The received baseband signal is sampled with a sampling offsett_(o) and a rate Nƒ_(s) and a block of its N subsequent samples[y(t_(o)), y(t_(o)+T), . . . , y(t_(o)+(N−1)T)] (with$\left( {{{with}\quad T} = \left. \frac{1}{{Nf}_{s}} \right)} \right.$

[0018] is subject to a fast fourier transform (FFT) of size N. Lety=[y₁, . . . , y_(N)]^(T) be the vector of N FFT samples so that$\begin{matrix}{y_{k} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{y\left( {t_{o} + {nT}} \right)}{{\exp \left( {{- }\quad 2\pi \quad {{kn}/N}} \right)}.}}}}} & (4)\end{matrix}$

[0019] After substituting (2) into (4) and using the approximation (3),we obtain $\begin{matrix}{{y_{k} = {{a_{k}s_{k}} + {\sum\limits_{l = 0}^{N - 1}{d_{l}s_{l}{\sum\limits_{n = 0}^{N - 1}{\left( {n/N} \right){\exp \left( {{- {{2\pi}\left( {k - l} \right)}}{n/N}} \right)}}}}} + n_{k}}},} & (5)\end{matrix}$

 a ₁=exp(i2πƒ_(s) lt ₀)(H _(l)(t _(r))+H _(l)(t ₀ −t _(r))),  (6)

d ₁=exp(i2πƒ_(s) lt ₀)TH_(l) ^(′)(t _(r)),  (7)

[0020] wherein n_(k), for 1≦k≦N, are the samples of AWGN having acertain variance σ². It is convenient to rewrite the result (5) in aclose matrix form. To this end, we define diagonal matrices A=diag{a₁, .. . , a_(N)}, D=diag{d₁, . . . , d_(N)} and an N×N matrix$\begin{matrix}{{\Xi = \left\{ \Xi_{p,q} \right\}_{p,{q = 1}}^{N}},{\Xi_{p,q} = {\sum\limits_{n = 0}^{N - 1}{\left( {n/N} \right){{\exp \left( {{- }\quad 2{\pi \left( {p - q} \right)}{n/N}} \right)}.}}}}} & (8)\end{matrix}$

[0021] With this notation, the expression (5) is equivalent to

y=As+ΞDs+n,  (9)

[0022] wherein n=[n₁, . . . , n_(N)]^(T) is an N×1 vector of AWGN. Inthe channel model (9), the effect of the channel is represented by twosets of N parameters a=[a₁, . . . , a_(N)]^(T) and d=[d₁, . . . ,d_(N)]^(T). Check that H_(l)(t_(r))+H_(l)^(′)(t_(r))(t_(o)−t_(r))≈H_(l)(t_(o)), hence the coefficients a_(k), for1≦k≦N ,are equal to the complex amplitudes of the channel frequencyresponse rotated by the sampling phase exp(i2πƒ_(s)lt₀). Similarly, thecoefficients d_(k), for 1≦k≦N, are equal to the time-domain derivativesof the complex amplitudes of the channel frequency response scaled bythe sampling period T and rotated by the same sampling phaseexp(i2πƒ_(s)lt₀).

[0023] Note that an inter-carrier interference occurs when the channelresponse varies in time (i.e. d≠0). This interference is defined by thevector d as well as the fixed N×N matrix Ξ. It can be is easily seenthat according to (8) the latter matrix is a Toeplitz Hermitian matrixand that${\Xi = \left\{ \Xi_{p,q} \right\}_{p,{q = 1}}^{N}},{\Xi_{p,q} = \left\{ \begin{matrix}{{\left( {N - 1} \right)/2},} & {{p = q};} \\{{- \left( {1^{{{2\pi}{({q - p})}}/N}} \right)^{- 1}},} & {p \neq {q.}}\end{matrix} \right.}$

[0024] Later in this document, we will call a the (vector of)amplitudes, d the (vector of) derivatives and Ξ the leakage matrix.

[0025] To process the received signal, the set of channel parameters aand d should be estimated. The estimation accuracy of these 2N scalarparameters may be enhanced if the statistical properties of the channelare used. First of all, we assume that channel variations are slowenough so that H_(k) ^(′)(t) do not change substantially within theduration of a symbol. In this case, we may rewrite (6) and (7) asfollows:

a ₁≈exp(i2πƒ_(s) lt _(o))H _(l)(t _(o)), d _(l)≈exp(i2πƒ_(s) lt _(o))TH_(l) ^(′)(t _(o)), 1≦l≦N.  (10)

[0026] Let us analyze the relationship between the quantities a, d andphysical parameters of the propagation channel, namely the set of its Kpropagation delays {τ₀, . . . , τ_(K)}, the corresponding Doppler shifts{ƒ₀, . . . , ƒ_(K)}, and complex amplitudes {h₀, . . . , h_(K)}. Notethat the statistical properties of the channel frequency response dependon the relative delays and Doppler shifts whereas the group delay and/orDoppler shift result in rotations of h_(k), for 1≦k≦K; these rotationsare handled by time and carrier synchronization/tracking. Hence, we mayassume without loss of generality that τ₀=0 and ƒ₀=0. Now, the channelfrequency response H_(l), and its derivative H_(l) ^(′) may be writtenas follows: $\begin{matrix}{{{H_{l}(t)} = {\sum\limits_{n = 0}^{K}{h_{n}{\exp \left( {\quad 2{\pi \left( {{f_{n}t} - {f_{s}l\quad \tau_{n}}} \right)}} \right)}}}},{{H_{l}^{\prime}(t)} = {i\quad 2\pi {\sum\limits_{n = 0}^{K}{f_{n}h_{n}{\exp \left( {{2\pi}\left( {{f_{n}t} - {f_{s}l\quad \tau_{n}}} \right)} \right)}}}}},{1 \leq l \leq {N.}}} & (11)\end{matrix}$

[0027] The relationships (10) and (11) may be readily used to deduce thestatistical properties of the amplitudes a and derivatives d. Wheneverthe number of propagation paths is big enough (ideally K>>N ), the setof coefficients {H_(l)(t), H_(l) ^(′)(t)}_(1≦l≦N) may be consideredjointly Gaussian distributed. Moreover, one can show that the sets{H_(l)(t)}_(1≦l≦N) and {H_(l) ^(′)(t)}_(1≦l≦N) are mutually uncorrelatedwhen the sets {h_(k)}_(1≦k≦K) and {ƒ_(k)}_(1≦k≦K) are statisticallyindependent and the Doppler spectrum has a symmetric shape. In thiscase, the vectors a and d may be assumed statistically independentmultivariate Gaussian with zero mean and covariance matrices

E{aa ^(H) }=C _(a) , E{dd ^(H) }=C _(d)  (12)

[0028] where E{·} stands for the mathematical expectation operator andC_(a), C_(d) are N×N Hermitian non-negative definite matrices.

[0029] An important particular case of C_(a) and C_(d) corresponds to astandard model for mobile channels, as described in the book MicrowaveMobile Communications by C. Jakes, John Wiley & Sons, Inc., 1974. Thismodel (known as Jakes model) assumes independent contributions ofdifferent propagation paths, an exponential delay profile and uniformlydistributed angles of incidence for different paths. One can show thatin this case, $\begin{matrix}{{C_{a} = C},{C_{d} = {\gamma^{2}C}},{\gamma^{2} = {\frac{1}{2}\left( {2\pi \quad f_{\Delta}T} \right)^{2}}},{C_{pq} = \frac{1}{1 + {{{2\pi}\left( {p - q} \right)}f_{s}T_{\Delta}}}},{1 \leq p},{q \leq N},} & (13)\end{matrix}$

[0030] wherein ƒ_(Δ) is the magnitude of the Doppler spread and whereinT_(Δ) is the root mean square propagation delay spread. The last twoparameters depend on the mobile velocity and propagation environmentrespectively.

[0031] Although the outlined channel model is characterized by 2Nparameters, the number of independent degrees of freedom issubstantially smaller in practice. This property comes from the factthat the propagation delay spread is often much smaller than the wordduration. This property also means that the entries of a are stronglycorrelated, to the extend that the covariance matrix C_(a) may beaccurately approximated by a low-rank matrix. Similarly, the entries ofd are strongly correlated and the covariance matrix C_(d) may also beaccurately approximated by a low-rank matrix. Let us consider the Jakesmodel and therefore (13). Define the eigendecomposition of C:

C=UΛU ^(H),  (14)

[0032] wherein U is the N×N unitary matrix of eigenvectors of C andwherein Λ is the N×N positive diagonal matrix of its eigenvalues {Λ₁, .. . , Λ_(N)}. Assume that the eigenvalues are ordered so that thesequence {Λ₁, . . . , Λ_(N)} is non-increasing. Under Jakes model, theelements of this sequence have an exponentially decaying profile:

Λ_(k)˜exp(−ƒ_(s)T_(Δ)k), for 1≦k≦N.  (15)

[0033] Hence, the sequence of eigenvalues may be accurately approximatedwith a relatively small number r of non-zero values: {Λ₁, . . . ,Λ_(N)}≈{Λ₁, . . . , Λ_(r),0 . . . 0}.

[0034] Our goal is to estimate the amplitudes a and the derivatives dfrom the received signals y. We will assume that the input symbols s areknown. It is easy to see that the total number of amplitudes andderivatives is equal to 2N which is twice as large as the number ofsubcarriers. This yields an accurate approximation of the vectors a andd by r degrees of freedom only. In other words, we may write

a≈Vh, d≈Vg,  (16)

[0035] where h and g are r×1 vectors that stack the free parameterscorresponding to the amplitudes and the derivatives respectively whereasthe N×r matrix V is built of the first r columns of U. With thisapproximation, a joint estimation of a and d becomes equivalent to ajoint estimation of h and g. Hence the total number of free parametersbecomes 2r instead of 2N. This observation has a crucial meaning takinginto account that a relatively small r is sufficient in practice suchthat r<<N.

[0036] An additional complexity reduction is due to the fact that theleakage matrix Ξ is diagonalized by a Fourier basis, i.e. that

Ξ=FΔF ^(H),  (17)

[0037] where F is the N-point FFT matrix with normalized columns and Δis a positive diagonal matrix. The aforementioned property of the matrixΞ follows directly from (8). Check that the diagonal values of Δ aregiven by the integers {0, 1, 2, . . . ,N−1}. Hence, a multiplication bythe N×N matrix Ξ may be implemented by a combination of N-point FFT(IFFT) and N pointwise multiplications, thereby substantially reducingcomplexity.

[0038] The approximation (16), together with the expression (17) lead toan optimal least square estimation procedure which is derived in thefollowing paragraphs.

[0039] Let us rewrite expression (9) so as to concentrate the channelparameters in two N×1 vectors: a for the amplitudes and d for thederivatives:

y=Sa+ΞSd+n,  (18)

[0040] where S is the N×N diagonal matrix with the values ŝ₁, . . . ,ŝ_(N) on its diagonal. To make use of a finite order channelapproximation, we will substitute (16) into (18). Furthermore, we alsosubstitute (17) into (18), in order to take into account the structureof the leakage matrix Ξ. The result of the two substitutions is asfollows:

y=SVh+FΔF ^(H) SVg+n,  (19)

[0041] A computationally attractive variant of (19) may be obtained bymoving from the frequency domain to the time domain. Namely, the N×1vector y=F^(H)y is the IFFT of the vector of subcarriers, therefore itstands for the received signal in the time domain (up to anormalization). Similarly, we define the N×1 vector of noise n in thetime domain. Recall that the noise is AWGN of power σ² in time as wellas in the frequency domain.

[0042] After applying the IFFT to (19), we obtain

y=Ph+ΔPg+n, where P=F ^(H) SV, n=F ^(H) n.  (20)

[0043] Here P is an N×r matrix. To derive the approximate MMSE estimate,we note that, according to (12), (13) and (14) and given anapproximation order r, the covariance matrices of h and g (as defined in(16)) satisfy

E{hh ^(H) }=Λ, E{gg ^(H)}=γ² Λ,  (21)

[0044] where Λ is the r×r diagonal matrix with the diagonal values {Λ₁,. . . , Λ_(r)}. Given the data model (20)-(21), the MMSE estimator ofthe parameters h and g yields the estimates ĥ and ĝ obtained byminimizing $\begin{matrix}{{{\sigma^{- 2}{{\underset{\_}{y} - {\left\lbrack {P,{\Delta \quad P}} \right\rbrack \begin{bmatrix}h \\g\end{bmatrix}}}}^{2}} + {{\begin{bmatrix}h \\g\end{bmatrix}^{H}\begin{bmatrix}{\underset{\_}{\Lambda}}^{- 1} & 0 \\0 & {\gamma^{- 2}{\underset{\_}{\Lambda}}^{- 1}}\end{bmatrix}}\begin{bmatrix}h \\g\end{bmatrix}}},} & (22)\end{matrix}$

[0045] over {h,g}. The aforementioned problem permits an explicitsolution given by the following expression: $\begin{matrix}{\begin{bmatrix}\hat{h} \\\hat{g}\end{bmatrix} = {{\begin{bmatrix}{{\sigma^{2}{\underset{\_}{\Lambda}}^{- 1}} + {P^{H}P}} & {P^{H}\Delta \quad P} \\{P^{H}\Delta \quad P} & {{\sigma^{2}\gamma^{- 2}{\underset{\_}{\Lambda}}^{- 1}} + {P^{H}\Delta^{2}P}}\end{bmatrix}^{- 1}\begin{bmatrix}P^{H} \\{P^{H}\Delta}\end{bmatrix}}\underset{\_}{y}}} & (23)\end{matrix}$

[0046] Finally, the empirical vectors of amplitudes and derivatives arecomputed, according to (16), via

â=Vĥ, {circumflex over (d)}=Vĝ.  (24)

[0047] The algorithm summarized in (23) and (24) is schematicallypresented in FIG. 2. Recall that Δ is diagonal matrix, i.e. applyingthis matrix to a vector yields N multiplications only. Hence, formoderate r, the main computational effort is related with computingP^(H)P, P^(H)ΔP and P^(H)Δ²P.

[0048]FIG. 1 shows a block diagram of a transmission system according tothe invention. The transmission system comprises a transmitter 10 and areceiver 20. The transmission system may comprise further transmitters10 and receivers 20. The transmitter 10 transmits a multicarrier signalvia a wireless channel to the receiver 20. The multicarrier signal maybe an OFDM signal or a MC-CDMA signal. The receiver 20 comprises ademodulator 22 for demodulating the received multicarrier signal 23,which received multicarrier signal 23 comprises vectors of receivedsymbols 23. The demodulator 22 may be implemented by means of a FFT. Thedemodulated multicarrier signal is supplied by the demodulator 22 to anequalizer 24. The equalizer 24 cancels intercarrier interference whichmay be included in the received multicarrier signal. The equalizer 24outputs vectors of estimated symbols 25 (which have been derived fromthe vectors of received symbols) to a (soft) slicer 26. The slicer 26produces soft metrics (soft decisions) and/or binary estimates (harddecisions) of the (coded) bits to be used in the further signalprocessing parts of the receiver (which are not shown), e.g. a FECdecoder. The output signal of the slicer 26 may also be regarded ascomprising estimated symbols 27. The receiver 20 further comprises achannel estimator 28 for estimating amplitudes 29 of the subcarriers andfor estimating time derivatives 29 of the amplitudes. The equalizer 24cancels the intercarrier interference included in the received(demodulated) multicarrier signal in dependence on the estimatedamplitudes and derivatives 29 which are supplied by the channelestimator 28 to the equalizer 24. The channel estimator 28 comprises areduced complexity filter for deriving vectors of the estimatedamplitudes and derivatives 29 from the vectors of received symbols 23and vectors of estimated symbols 27.

[0049] The estimator 28 is described by equations (23)-(24); itsblock-diagram is shown in FIG. 2. Vector components of a vector of Nestimated symbols 27 multiply N rows of the N×r matrix V in a row-wisemultiplier 40. The r columns of the resulting N×r matrix undergo an IFFT42. The resulting N×r matrix P is supplied to a matrix multiplier 46, toa matrix multiplier 44 and to a matrix multiplier 52. The matrixmultiplier 46 computes the product ΔP which is a row-wise multiplicationof the N×r matrix P by N diagonal entries of Δ. The resulting N×r matrixis supplied to a matrix multiplier 48. In this matrix multiplier 48 ther×N Hermitian conjugate P^(H)Δ of the output of matrix multiplier 46 ismultiplied by a N×1 vector of received signals 23. The output signal ofthe matrix multiplier 48 is supplied to a first input of a stacker 56.

[0050] In the matrix multiplier 44 the products P^(H)P, P^(H)ΔP andP^(H)Δ²P are computed from the outputs P and ΔP of the IFFT 42 and thematrix multiplier 46 respectively. The quantities σ² Λ ⁻¹ and σ²γ⁻² Λ ⁻¹are added to the blocks P^(H)P and P^(H)Δ²P respectively in a matrixadder 50. The output signal of the matrix adder 50 is a 2r×2r matrixthat appears in the equation (23). This matrix is inverted in a matrixinverter 54 and the resulting inverted matrix is supplied to a matrixmultiplier 58.

[0051] In the matrix multiplier 52 the r×N Hermitian conjugate P^(H) ofthe output of The IFFT 42 is multiplied by the N×1 vector of receivedsignals 23. The resulting signal is supplied to a second input of thestacker 56. The stacker 56 stacks the signals which are supplied to itsfirst r×1 and second r×1 input vector and the stacked 2r×1 vector isthereafter supplied to the matrix multiplier 58 which multiplies it withthe 2r×2r inverted matrix. The output 2r×1 signal of the matrixmultiplier 58 is next supplied to a splitter 60 which splits it into twor×1 vectors. Each of these two vectors is thereafter multiplied by amatrix V in the matrix multipliers 62 and 64. The resulting output r×1vectors are the estimated amplitudes and derivatives 29.

[0052] The proposed channel estimator uses the N×1 vector y of receivedsymbols in the time domain (i.e. before OFDM demodulation) and the N×1vector ŝ of the transmitted symbols or their estimates. The algorithmalso makes use of the channel statistics represented by V and Λ as wellas leakage matrix properties that are concentrated in Δ. Note that thesethree quantities may be precomputed.

[0053] Let us briefly analyze the complexity of the proposed procedure.The most computationally extensive blocks of the scheme are the matrixmultiplier 44 and the matrix inverter 54. The matrix multiplier 44computes a 2r×2r matrix built of auto- and cross-products of two N×rmatrices (e.g. P^(H)P, P^(H)ΔP and P^(H)Δ⁰P).These operations require 3r(r+1)N/2 complex-valued multiplications. The matrix inverter 54 invertsa2r×2r matrix, which yields approximately ⅔(2r)³=16r³/3 complexmultiplications. Hence, the overall complexity grows only linearly alongwith the number N of subcarriers. The last feature is particularlyattractive for DVB-T where N ranges from 2048 in the 2K-mode to 8192 in8K-mode.

[0054] Simulations have shown that the proposed estimation of a and dyields a loss of approximately 1.5 dB when r=5 compared to the situationin which the channel parameters are known. The loss becomes negligibleat r=10.

[0055] The proposed channel response estimation algorithm relies uponthe knowledge of the whole set of input symbols for at least one OFDMblock. The application of the algorithm becomes straightforward when sis known to the receiver (i.e. during the training phase). During thedata transmission phase, the following ways to obtain the referencesignal may be considered:

[0056] (A) Fast channel variations: in this scenario, the channelcoherence time is supposed to be smaller or comparable to the time delaybetween adjacent OFDM blocks. In this case, we assume that a channelestimate corresponding to a given block can not be reused during thefollowing block in a satisfactory way, i.e. so that a required low levelBER is preserved. We may suggest either to use the estimate from theprevious block and along with the simplified MMSE solution or to applythe conventional OFDM processing in order to obtain the estimate ŝ ofthe transmitted symbols. This estimate is subsequently used to refreshthe channel estimate. Although the input symbols ŝ are detected withsome errors, the impact of these errors on the estimation accuracy isnot very important. Indeed, these errors will result in an equivalentadditive noise with an average power that is comparable to the power ofthe observation noise. The impact of this additional noise on theestimation accuracy is alleviated by the fact that the number N ofobservation samples is substantially bigger than the number 2r of freeparameters to be estimated.

[0057] (B) Slow channel variations: in this case we assume that thechannel coherence time is substantially bigger than the time delaybetween the adjacent OFDM blocks. Therefore, the channel estimate fromthe current OFDM block may be reused for a number of the followingblocks. In this case, the channel estimate is periodically computedaccording to the defined procedure. This estimate makes use of thedetected data corresponding to the current OFDM block and may beexploited for the following OFDM blocks. The periodicity of estimationis defined by the channel coherence time. This scheme enables arelatively cheap real time implementation since a processing delay equalto the duration of several consecutive OFDM blocks is possible.

[0058] In the described estimation procedure, a single OFDM block isused for the channel estimation. Although a single block enables rathergood estimation accuracy in DVB-T (owing to the fact that the number ofsubcarriers is much bigger than the number of free channel parameters inboth 2K and 8K mode), the use of multiple OFDM blocks may be alsoconsidered. The extension to the case of multiple blocks is ratherstraightforward: it consists of stacking a number of matrices P computedfrom the corresponding OFDM blocks. The rest of the procedure remainsunaltered. The corresponding increase in the computation complexity islinear with respect to the number of blocks involved.

[0059] Although in the above mainly an OFDM transmission system isdescribed, the invention is also and equally well applicable to othermulticarrier transmission systems such as MC-CDMA transmission systems.The reduced complexity filter may be implemented by means of digitalhardware or by means of software which is executed by a digital signalprocessor or by a general purpose microprocessor.

[0060] The scope of the invention is not limited to the embodimentsexplicitly disclosed. The invention is embodied in each newcharacteristic and each combination of characteristics. Any referencesign do not limit the scope of the claims. The word “comprising” doesnot exclude the presence of other elements or steps than those listed ina claim. Use of the word “a” or “an” preceding an element does notexclude the presence of a plurality of such elements.

1. A transmission system for transmitting a multicarrier signal from atransmitter (10) to a receiver (20), the multicarrier signal comprisinga plurality of subcarriers, the receiver (20) comprising a channelestimator (28) for estimating amplitudes of the subcarriers and forestimating time derivatives of the amplitudes, the receiver (20) furthercomprising an equalizer (24) for canceling intercarrier interferenceincluded in the received multicarrier signal in dependence on theestimated amplitudes and derivatives (29), wherein the channel estimator(28) comprises a reduced complexity filter for deriving vectors of theestimated amplitudes and derivatives (29) from vectors of receivedsymbols (23) and vectors of estimated symbols (27).
 2. The transmissionsystem according to claim 1, wherein the reduced complexity filter isarranged for exploiting an amplitude correlation between the amplitudesof different subcarriers and/or for exploiting a derivative correlationbetween the derivatives of different subcarriers.
 3. The transmissionsystem according to claim 2, wherein the amplitude correlation and/orthe derivative correlation are characterized by a N×N matrix C, with Nbeing the number of subcarriers, wherein C=UΛU^(H), with U being the N×Nunitary matrix of eigenvectors of C and Λ being the N×N positivediagonal matrix of the eigenvalues {Λ₁, . . . , Λ_(N)} of C, and whereinΛ is approximated by {Λ₁, . . . , Λ_(r),0, . . . 0}, with r<<N.
 4. Thetransmission system according to claim 2 or 3, wherein the reducedcomplexity filter comprises a multiplication by the N×N leakage matrixΞ, wherein the multiplication is implemented by a combination of anN-point IFFT (42) and an N pointwise multiplier (46).
 5. A receiver (20)for receiving a multicarrier signal from a transmitter (10), themulticarrier signal comprising a plurality of subcarriers, the receiver(20) comprising a channel estimator (28) for estimating amplitudes ofthe subcarriers and for estimating time derivatives of the amplitudes,the receiver (20) further comprising an equalizer (24) for cancelingintercarrier interference included in the received multicarrier signalin dependence on the estimated amplitudes and derivatives (29), whereinthe channel estimator (28) comprises a reduced complexity filter forderiving vectors of the estimated amplitudes and derivatives (29) fromvectors of received symbols (23) and vectors of estimated symbols (27).6. The receiver (20) according to claim 5, wherein the reducedcomplexity filter is arranged for exploiting an amplitude correlationbetween the amplitudes of different subcarriers and/or for exploiting aderivative correlation between the derivatives of different subcarriers.7. The receiver (20) according to claim 6, wherein the amplitudecorrelation and/or the derivative correlation are characterized by a N×Nmatrix C, with N being the number of subcarriers, wherein C=UΛU^(H),with U being the N×N unitary matrix of eigenvectors of C and Λ being theN×N positive diagonal matrix of the eigenvalues {Λ₁, . . . , Λ_(N)} ofC, and wherein Λ is approximated by {Λ₁, . . . , Λ_(r),0, . . . 0}, withr<<N.
 8. The receiver (20) according to claim 6 or 7, wherein thereduced complexity filter comprises a multiplication by N×N leakagematrix Ξ, wherein the multiplication is implemented by a combination ofan N-point IFFT (42) and an N pointwise multiplier (46).
 9. A channelestimator (28) for estimating amplitudes of subcarriers included in amulticarrier signal and for estimating time derivatives of theamplitudes, the channel estimator (28) comprising a reduced complexityfilter for deriving vectors of the estimated amplitudes and derivatives(29) from vectors of received symbols (23) and vectors of estimatedsymbols (27).
 10. The channel estimator (28) according to claim 9,wherein the reduced complexity filter is arranged for exploiting anamplitude correlation between the amplitudes of different subcarriersand/or for exploiting a derivative correlation between the derivativesof different subcarriers.
 11. The channel estimator (28) according toclaim 10, wherein the amplitude correlation and/or the derivativecorrelation are characterized by a N×N matrix C, with N being the numberof subcarriers, wherein C=UΛU^(H), with U being the N×N unitary matrixof eigenvectors of C and Λ being the N×N positive diagonal matrix of theeigenvalues {Λ₁, . . . , Λ_(N)} of C, and wherein Λ is approximated by{Λ₁, . . . , Λ_(r),0, . . . 0}, with r<<N.
 12. The channel estimator(28) according to claim 10 or 11, wherein the reduced complexity filtercomprises a multiplication by the N×N leakage matrix Ξ, wherein themultiplication is implemented by a combination of an N-point IFFT (42)and an N pointwise multiplier (46).
 13. A method of estimatingamplitudes of subcarriers included in a multicarrier signal and forestimating time derivatives of the amplitudes, the method comprisingfiltering vectors of received symbols (23) and vectors of estimatedsymbols (27) with a reduced complexity filter in order to derive vectorsof the estimated amplitudes and derivatives (29).
 14. The methodaccording to claim 13, wherein the reduced complexity filter is arrangedfor exploiting an amplitude correlation between the amplitudes ofdifferent subcarriers and/or for exploiting a derivative correlationbetween the derivatives of different subcarriers.
 15. The methodaccording to claim 14, wherein the amplitude correlation and/or thederivative correlation are characterized by a N×N matrix C, with N beingthe number of subcarriers, wherein C=UΛU^(H), with U being the N×Nunitary matrix of eigenvectors of C and Λ being the N×N positivediagonal matrix of the eigenvalues {Λ₁, . . . , Λ_(N)} of C, and whereinΛ is approximated by {Λ₁, . . . , Λ_(r)0, . . . 0}, with r<<N.
 16. Themethod according to claim 14 or 15, wherein the reduced complexityfilter comprises a multiplication by the N×N leakage matrix Ξ, whereinthe multiplication is implemented by a combination of an N-point IFFT(42) and an N pointwise multiplier (46).